I applied to RVC, Nottingham, Liverpool and Surrey without meeting their GCSE requirements
Received interviews/offers from the other three but Surrey was a flat out rejection.
It certainly makes you a weaker applicant but provided your work experience, A levels (I applied with actual results not just predictions) and personal statement is good I wouldn't rule out your chances.
Of course this depends how close you were too them - I only missed I think two GCSE targets by a grade